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Modular Forms and Weierstrass Mock Modular Forms [PDF]
Mathematics, 2016 Alfes, Griffin, Ono, and Rolen have shown that the harmonic Maass forms arising from Weierstrass ζ-functions associated to modular elliptic curves “encode” the vanishing and nonvanishing for central values and derivatives of twisted Hasse-Weil L ...
Amanda Clemm
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Mock modular forms as $p$-adic modular forms [PDF]
Transactions of the American Mathematical Society, 2010 In this paper, we consider the question of correcting mock modular forms in order to obtain $p$-adic modular forms. In certain cases we show that a mock modular form $M^+$ is a $p$-adic modular form.
Bringmann, Kathrin +2 more
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Lifting of Modular Forms [PDF]
Publications mathématiques de Besançon. Algèbre et théorie des nombres, 2019 The existence and construction of vector-valued modular forms (vvmf) for any arbitrary Fuchsian group $\mathrm{G}$, for any representation $\rho:\mathrm{G} \longrightarrow \mathrm{GL}_{d}(\mathbb{C})$ of finite image can be established by lifting scalar ...
Bajpai, Jitendra
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Introduction to Modular Forms [PDF]
, 2015 We introduce the notion of modular forms, focusing primarily on the group PSL2Z. We further introduce quasi-modular forms, as wel as discuss their relation to physics and their applications in a variety of enumerative problems. These notes are based on a lecture given at the Field's institute during the thematic program on Calabi-Yau Varieties ...
Rose, S.
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Holomorphic subgraph reduction of higher-point modular graph forms
Journal of High Energy Physics, 2019 Modular graph forms are a class of modular covariant functions which appear in the genus-one contribution to the low-energy expansion of closed string scattering amplitudes.
Jan E. Gerken, Justin Kaidi
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, 2016 We survey the progress (or lack thereof!) that has been made on some questions about the p-adic slopes of modular forms that were raised by the first author in [Buz05], discuss strategies for making further progress, and examine other related questions ...
Buzzard, Kevin, Gee, Toby
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On the Modularity of Normal Forms in Rewriting
Journal of Symbolic Computation, 1996 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Massimo Marchiori
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Seven Small Simple Groups Not Previously Known to Be Galois Over
Mathematics, 2022 In this note we realize seven small simple groups as Galois groups over Q. The technique that we employ is the determination of the images of Galois representations attached to modular and automorphic forms, relying in two cases on recent results of ...
Luis Dieulefait +2 more
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On the modularity of certain functions from the Gromov–Witten theory of elliptic orbifolds [PDF]
Royal Society Open Science, 2015 In this paper, we study modularity of several functions which naturally arose in a recent paper of Lau and Zhou on open Gromov–Witten potentials of elliptic orbifolds.
Kathrin Bringmann +2 more
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Modular flavor symmetry and vector-valued modular forms
Journal of High Energy Physics, 2022 We revisit the modular flavor symmetry from a more general perspective. The scalar modular forms of principal congruence subgroups are extended to the vector-valued modular forms, then we have more possible finite modular groups including Γ N and Γ N ′ $$
Xiang-Gan Liu, Gui-Jun Ding
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